Semi-permeable membrane for use in osmosis

ABSTRACT

The present invention concerns a semi-permeable membrane for use in osmosis consisting of one thin layer of a non-porous material (the diffusion skin), and one or more layers of a porous material (the porous layer), where the porous layer has a structure where porosity φ, thickness of the porous layer (m), and tortuosity τ, are related to one another as given by the expression: 
     
       
      
       x·τ=φ·S  
      
     
     wherein S is a structure parameter having a value equal to or less than 0.0015 meter. 
     Further a method for providing elevated pressure by osmosis as well as a device for providing an elevated osmotic pressure and electric power is described.

This application is a Continuation of co-pending U.S. patent applicationSer. No. 12/068,185 filed on Feb. 4, 2008, which is a Continuation ofco-pending U.S. patent application Ser. No. 10/343,735 filed on Jun. 30,2003. Application Ser. No. 10/343,735 is the National Phase ofPCT/NO2001/00314 filed on Jul. 20, 2001, which claims priority under 35U.S.C. 119(e) to U.S. Provisional Application No. 60/228,778 filed onAug. 29, 2000, and claims priority under 35 U.S.C. 119(a) to PatentApplication No. 20003977 filed in Norway on Aug. 4, 2000, all of whichare hereby expressly incorporated by reference into the presentapplication.

The present invention concerns an improved semi-permeable membrane foruse in osmosis with properties adapted to the object, and/or membranemodules with reduced loss of energy. More detailed the inventionconcerns as semi-permeable membrane consisting of one thin layer of anon-porous material (the diffusion skin), and one or more layers of aporous material (the porous layer). Further, the invention concerns amethod for providing elevated pressure by osmosis (from salt gradients)in a system with pressure retarded osmosis through one or moresemi-permeable membranes, which are built up of several layers, wherebyat least a part of the elevated osmotic pressure is maintained in thesystem. A plant for providing an osmotic elevated pressure and electricpower is also described.

U.S. Pat. No. 4,283,913 comprises a saturated non-convective waterreservoir which captures solar energy and which is used as a separationunit in combination with reverse electro dialysis or pressure retardedosmosis for energy production. From the water reservoir which partly canseparate a solution, a higher concentrated stream and a lessconcentrated stream is passed into two chambers separated with asemi-permeable membrane. Parts of the energy which is created bypermeation of the stream with lower concentration through the membraneand the subsequent mixing of the two mentioned streams are transformedinto energy before the streams are returned to the water reservoir.

From U.S. Pat. No. 4,193,267 it is known a procedure and an apparatusfor the production of power by pressure retarded osmosis, wherein aconcentrated solution with high hydraulic pressure is passed along asemi-permeable membrane, and where a diluted solution is passed alongthe opposite side of said membrane. A portion of the diluted solution istransported through the membrane and creates a pressurized mixedsolution. The potential energy stored in this pressurized mixture isconverted into applicable energy by pressure release and pressurizingthe diluted solution.

In U.S. Pat. No. 3,978,344 a procedure is described for producing energyby pressure retarded osmosis by the use of a turbine and asemi-permeable membrane. Further it is known from U.S. Pat. No.3,906,250 production of energy by pressure retarded osmosis by hydraulicpressurizing a first liquid which is introduced on one side of amembrane, where after another liquid with lower hydraulic pressure and alower osmotic pressure is introduced on the other side of a membrane.Pressure retarded osmosis will lead to transport of parts of the otherliquid through the semi-permeable membrane and thereby a pressurizedmixed solution is formed with a larger volume than the first liquidalone. The stored energy is then transformed in a turbine into useableenergy such as electric or mechanical power.

For centuries it has been known that when salt water and fresh water arepartitioned in two different chambers of a semi-permeable membrane, madefor example of a biological membrane, e.g. of hog's bladder, fresh waterwill press itself through the membrane. The driving force is capable ofelevating the salt water level above the level of the fresh water,whereby a potential energy is obtained in the form of a static waterheight. The phenomenon is called osmosis and belongs to the so-calledcolligative properties of a solution of a substance in anothersubstance. This phenomenon can be thermodynamically described and theamount of potential energy is therefore known. In a system of freshwater and ordinary sea water the theoretical potential expressed aspressure is approximately 26 bars. The energy potential can in principlebe utilized by several technical methods where the energy can berecovered as i.e. steam pressure and stretching of polymers. Two of thetechnical methods are using semi-permeable membranes, and these arereverse electro dialysis (energy potential as electrical DC voltage) andpressure retarded osmosis, PRO, (energy potential as water pressure).

Calculations have been made to find the costs of energy production atPRO plants. The uncertainty of such calculations is illustrated by thefact that reported values for the energy costs fluctuate over more thana magnitude. Wimmerstedt (1977) indicated a little more than 1 NOK/kWh,whereas Lee et. al. (1981) indicated prohibitive costs. Jellinek andMasuda (1981) indicated costs of less than 0.13 NOK/kWh. Thorsen (1996)made a cost estimate which stated 0.25-0.50 NOK/kWh based on anevaluation of recent data for membrane properties and prices. All ofthese evaluations are based on the use of fresh water and sea water.Thus, earlier conclusions indicated costs of energy produced by PRO thatvaried very much. A comprehensive elucidation of methods for energyproduction today and in the future is included in the book “RenewableEnergy” (ed. L. Burnham, 1993) prior to the Rio conference aboutenvironment and development. Here salt power is only mentioned verybriefly, and it is maintained that the costs are prohibitive.

When fresh water is mixed with salt water there is an energy potential(mixing energy) for PRO corresponding to a downfall of 260 meters forfresh water, and the locations of most interest are rivers flowing intothe ocean. In the present invention it has been found that 35-40% ofthis energy can be recovered by PRO. In a practical power plant theenergy will be liberated as water pressure by approximately 10 bars inthe stream of brackish water which develops after the fresh and saltwater have been mixed together. This pressure can be used for operatingconventional turbines. The effective amount of energy will then bebetween 50 and 100% of the naturally occurring downfall energy in freshwater on world basis.

According to the present invention the actual potential for amounts ofpower seems to be 25-50% of the water power which today has beendeveloped in Norway. Power plants based on the present invention do notlead to significant emissions into the air or water. Further this formof energy is fully renewable, and is only using natural water as drivingforce in the same manner as conventional water power plants. The objectof the present invention is to make possible commercial utilization ofsalt power on a bigger scale.

Assumed area expenditure for an intended salt power plant will berelatively small and in the same magnitude as for a gas power plant, andsubstantially smaller than for wind power. The method is thereforeespecially friendly to the environment. Briefly the method with regardto the environmental effects and the use properties can be characterisedas follows:

-   -   no CO₂ emissions or other big quantities of emissions other than        water    -   renewable, like conventional power from water    -   stable production, unlike the wind and wave power    -   small areas are required, a fact which leads to little influence        on the landscape    -   flexible operation    -   suited for small as well as large plants

Known art are not dealing with effective semi-permeable membranes withreduced loss of energy where the biggest part of the salt gradient inthe membrane is present in the same layer as the flow resistance if themembrane is used for PRO. Therefore an effective and optimisedmembrane/membrane module has to be developed where the requirement tosalt gradient in the membrane and flow resistance as mentioned above aresatisfied. This can not satisfactorily be achieved in existing membranesdesigned for filtering (reverse osmosis). Further a method forproduction of electric power from osmotic pressure with an effectivesemi-permeable membrane as mentioned above in a system with PRO where asatisfactory part of the osmotic pressure is maintained, has not beendescribed.

An important feature of the present invention is that most of the saltgradient in the membrane is localized in the same layer—the diffusionskin—as the flow resistance. Further the present patent application alsoconsists of a porous carrier material for the diffusion skin with noresistance worth mentioning against water transport and salt diffusion.This is not satisfactorily achieved in existing membranes designed forfiltering (reverse osmosis)/pressure retarded osmosis, PRO. In thepresent invention salt therefore does not appear in unfavourably highconcentrations in parts of the membrane other than the diffusion skin.According to the present invention membranes with particular innerstructures are also important. Further the concentration polarization ofsalt on the sea water side of the membranes is reduced compared toconventional membranes.

In the present PRO plant pressure energy in the brackish water isdirectly hydraulic recovered for pressurizing incoming sea water.Thereby a part of the loss which ordinarily would occur in an ordinarywater pump for this purpose is avoided. By avoiding this loss the PROplant according to the present invention can be built on ground levelinstead of below ground level and nevertheless achieve acceptableefficiency.

Recovery of pressure energy by direct hydraulic pressurizing of incomingsea water takes place in a device where the turbine pressure in half ofthe device is pushing sea water directly into the membrane module. Inthe other half the brackish water is pushed back and out of the PROplant as the sea water is pumped in. The mentioned processes which takeplace in the respective halves of the device for hydraulic pressurizingof sea water alternate by rotation of the water containing part or by acontrolled valve system in the mentioned device. The mentioned directhydraulic pressure transfer leads to that sea water pumps with limitedefficiency are no longer necessary.

The present invention describes semi-permeable membranes or membranemodules in which the membranes include a thin diffusion skin withnatural osmotic properties, and the rest of the membrane has anincreased porosity, so that salt is not collected here (the porouslayer).

The present invention comprises a semi-permeable membrane for use inosmosis consisting of one thin layer of a non-porous material acting asdiffusion skin, and at least one layer of a porous material, wherein theporous layer has a structure where porosity φ, thickness of the porouslayer×(m), and tortuosity τ, stand in relation to each other asindicated by the equation

x·τ=φ·S   Equation (1)

S is a structure parameter having a value equal to or less than 0.0015meter and can be expressed as S=x·τ/φ, which is a precise expression forthe structure in the porous part of the membrane.

The membrane is suitably configured for pressure retarded osmosis.

As will be appreciated by the average expert in the art, the value of Sis for a wetted membrane.

The porous layer of the membrane, when an amount of salt containingwater is brought contact with the non-porous material or diffusion skin,has properties related to a salt permeability parameter B (in thediffusion skin) defined by:

B=(φ·D·(dc/dx)/τ−J·c)·1/Δc _(s)   Equation (2)

wherein:

-   -   A is the water permeability,    -   B is the salt permeability (m/s),    -   Δc_(s) is the difference in salt concentration over the        diffusion skin (moles/cm³),    -   φ is the porosity,    -   x is the thickness of the porous layer (m),    -   J is the water flux (m/s),    -   c is the salt concentration (moles/cm³),    -   D is the diffusion coefficient of the salt (m²/s),    -   τ is the tortuosity,        where the efficiency of the membrane in pressure retarded        osmosis for a given value of a water permeability, A (m/s/Pa),        can be expressed by an integration of Equation (2) to yield:

Δc _(s) /c _(b)=exp(−d _(s) ·J/D)/{1+B·[(exp(d _(f) ·J/D+S·J/D)−exp(−d_(s) ·J/D)]/J}  Equation (3)

wherein:

-   -   c_(b) is the concentration of salt water salt minus the        concentration of salt in the fresh water (moles/cm³),    -   d_(f) and d_(s) are the thickness of the diffusion films        (concentration polarizing) on the fresh water side and salt        water side, respectively, of the membrane (μm),    -   Δc_(s)/c_(b) expresses the efficiency of the membranes in        pressure retarded osmosis for a given value of the water        permeability.

The value of the structure parameter S and thereby the inner structureof the membrane is decisive for its efficiency in pressure retardedosmosis. The structure should have only one thin and non-porous layerwherein salt has considerably lower diffusion velocity than water. Theother layers must all be porous so that salt and water can betransported with as little resistance as possible. Usually severalporous layers are present to give the membrane the correct mechanicalproperties and/or as a result of the production method. In those caseswhere the diffusion skin lies between two or more porous layers, or themembrane is laterally reversed in relation to fresh water and saltwater, the expressions will be more complicated, but the followingdiscussion will be valid in the same manner.

The structure parameter S should have a value of 0.0015 meter or lower.The thickness of the membrane is less than 150 μm, preferably less than100 μm. The average value for porosity, φ, in the porous layer in thepresent invention is more than 50%. The semi-permeable membrane has atortuosity, τ, which is less than 2.5. The permeability for salt, B, isless than 3·10⁻⁸ m/s, and the water permeability, A, is more than1·10⁻¹¹ m/s/Pa. The thickness of the diffusion film on the sidecontaining lesser salt and the side containing more salt is less than 60μm, preferably less than 30 μm.

Membrane modules according to the present invention comprise flowbreakers consisting of threads of polymers which are forming a net witha square or rhombic pattern. Further several membranes are packedtogether to modules (rolled up to spiral membranes) where the distancebetween adjacent membranes are from 0.4 to 0.8 mm.

The present invention further concerns a method where an elevatedpressure is provided by osmosis (from salt gradients) in a system withpressure retarded osmosis through one or more semi-permeable membranes,which are built up of several layers, where at least one part of theosmotic pressure is maintained in the system. The method includes

-   -   contacting a salt containing feed stream with a non-porous layer        (the diffusion skin) in one or more semi-permeable membranes;        where at the same time a feed stream containing less salt is        brought in contact with the other side of the diffusion skin,        and where an adjacent porous layer (the porous layer) in one or        more of the mentioned semi-permeable membranes has a structure        where the porosity φ, the thickness of the porous layer×(m), and        the tortuosity τ, are related to one another as indicated by the        expression

x·τ=φ·S

-   -    wherein S is a structure parameter which is equal to or less        than 0.0015 meter,    -   whereby water (H₂O) from the stream containing less salt        naturally is driven through the semi-permeable membrane by        osmosis and creates an osmotic hydraulic elevated pressure on        the permeate side.

In the stated method at least a part of the potential osmotic pressurebetween the two water streams is hydraulic transferred directly to theincoming salt containing feed stream. The amount of the salt containingfeed stream is 1-3 times higher than the amount of the feed streamcontaining less salt, so that the ratio between the length of a flowpath of the salt containing and the less salt containing stream is from0.3 to 1.0. The distance between adjacent membranes is from 0.4 to 0.8mm.

In the spiral modules the channels for the salt containing feed streamare 10-50% filled with one or more flow breaking devices consisting ofthreads of polymer which form a net with square or rhombic pattern.

The pressure in the salt containing feed stream on the membrane/membranemodules is in the area from 6-16 bars.

As an alternative to spiral membranes parallel fibres can be placed inlayers between successive streams of a less salt containing feed streamand a salt containing feed stream. The above mentioned will then be alittle altered, but the pressure will be the same.

The invention concerns in addition a plant wherein an elevated osmoticpressure is provided, and where the plant comprises one or moresemi-permeable membranes or membrane modules where the membranescomprise a non-porous layer (the diffusion skin) and at least one porouslayer; and an arrangement for direct hydraulic transmission of an-osmotic pressure.

Further referred to is also a plant for providing elevated osmoticpressure, suitably for the purpose of generating electric power. Theplant includes one or more semi-permeable membranes or membrane moduleswhere the membranes comprise a non-porous layer (the diffusion skin) andat least one porous layer; and an arrangement for direct hydraulictransmission of an osmotic pressure, and at least a turbine withelectric generator.

The plant can be placed on the ground, or below the surface of the earthdown to a level not below 200 meters.

Pressure retarded osmosis is like all osmotic processes based onselective mass transport through membranes. A chamber with fresh wateris separated from a chamber with sea water by a semi-permeable membrane.This membrane allows transport of water, but not of salt.

Both water and salt will diffuse from high to low concentration, but themembrane prevents the transport of salt. The result is a net watertransport from the fresh water side to the sea water side, and apressure is building up on the sea water side. Thus the osmotic watertransport is retarded by the building up of pressure. Water which hasbeen transported to the sea water side is there at a higher pressure,and work can be extracted if the water is allowed to flow out through aturbine. In this way the free energy by mixing fresh water and sea watercan be converted to work.

If fresh water is flowing into the sea water side without anythingflowing out, the pressure will build up. Finally, the pressure on thesea water side will be so high that the transport of water comes to astop. This happens when the difference in pressure equals the osmoticpressure of sea water given by van't Hoff's equation:

p _(osmotic)=2RTC _(NaCl)   Equation (4)

Here R is the gas constant and T is absolute temperature. For a 35 g/lNaCl solution equation (4) gives a theoretical osmotic pressure of 29bars at 20° C. This corresponds to a water column of 296 meters. If onemole water (0.018 kilos) is lifted 296 meters, a work of 52.2 J has tobe carried out.

In a power plant based on pressure retarded osmosis fresh water, beingfeed into the low pressure side, is transported by osmosis through thesemi-permeable membrane to the high pressure side. From the highpressure side the water is pressure released through a turbine whichgenerates mechanical power. To keep a necessary high salt concentrationon the sea water side, sea water has to be pumped in against the workingpressure. Net energy is produced because the volume stream which isexpanding (fresh water+sea water) is larger than the volume stream whichis compressed. Some of the fresh water is leaving the plant from the lowpressure side, and provides for the transport of contaminations awayfrom the fresh water and possible salt which has leaked out from thehigh pressure side.

Another possible design of a plant for pressure retarded osmosis is tobuild the plant buried 0-200 m, suitably 50-150 m, most preferably 120 mbelow ground level. In this case fresh water is passed through pipelinesdownwards to the turbines, and from there into the low pressure side ofthe membranes. Sea water is passed into the high pressure side of themembranes which has been pressurized by hydrostatic power, and the seawater can circulate through the high pressure side with friction as theonly loss. The fresh water will be transported through the membranedriven by the osmotic power, and leaves the plant mixed with sea water.The membranes can then be positioned as land based modules buried underground level together with the turbines and other equipment. If the seais more deep-set than the excavation the membrane modules could beplaced directly in the sea.

The skin of the membrane can possibly be located either against the seawater or the fresh water. Locating the diffusion skin against the freshwater side will have the advantage that the contaminations in the freshwater being more readily rejected on the membrane surface because thediffusion skin has far smaller pores in comparison with the porouscarrier. Since there is a net volume stream moving in towards themembrane on the fresh water side, this volume stream will be able totransport different types of impurities which can lead to fouling of themembrane. On the other hand, a continuous water stream from the membraneon the water side will contribute to keeping the surface of the membraneclean.

Because all of the pressure difference in the present process lies overthe non-porous material (the diffusion skin), it can be an advantagethat the diffusion skin lies on the sea water side since theoverpressure will press the diffusion skin against the carrier. With thediffusion skin on the fresh water side there is a risk that thediffusion skin is loosened from the carrier, and the membrane can bedestroyed.

Further, the parameters for the water permeability, A, and the saltpermeability, B, are of high importance as to the performance of themembrane.

For a membrane which is totally without salt leakage, the thickness,porosity and tortuosity of the carrier will not be of great importanceto the energy production.

It seems to be a considerable dependence on film thickness due toconcentration polarization on the sea water side alone, as concentrationpolarisation on the fresh water side is fully negligible for a membranewith a small salt leakage.

The thickness of this diffusion film is a critical size for the energyproduction by pressure retarded osmosis, This size has to be determinedexperimentally from transport trials where flux data are adapted to theactual model. Theoretical calculations with a more complex transportmodel indicate a thickness of the diffusion film of approximately0.000025 m.

The thickness of the diffusion film on the surface of the membraneagainst the sea water side can be reduced by increasing the flowvelocity on the sea water side, and by the use of devices which increasethe stirring of the flowing sea water (turbulence promoters). Suchefforts will increase the loss by friction during the flow of the seawater, and there will be an optimum point with regard to the sea waterrate through a membrane module and the shaping of the membrane module.

As mentioned above, the concentration polarization of salt will be asmall problem on the fresh water side in a good membrane module. This isa great advantage since the fresh water rate has to be low in parts of agood device as most of the fresh water is to be transported through themembrane and over to the sea water.

By pressure retarded osmosis the most important members of loss will bein connection with pressurizing sea water, pumping water through themembrane module and loss by conversion of pressure energy in water intoelectric energy by means of turbine and generator.

Because of friction loss a drop in pressure will develop over themembrane module. The water must be pumped through a narrow channel whichis provided with a distance net to keep the required width of thechannel, and which at the same time can promote mixing of the waterphase. Thus the thickness of the diffusion film can be reduced, and theefficiency in the PRO process can be improved.

In PRO processes with a good membrane module concentration polarizationwill only be an essential problem on the sea water side, since the saltconcentration on the fresh water side only shows a low increase.Further, the rate on the sea water side will be higher than on the freshwater side, because fresh water is transported over to the sea water,and also because there exists a desire to maintain the highest possiblesalt concentration in the sea water. The last mentioned is achieved byhaving a high through flow of salt water, but the profit of a high saltwater rate has to be considered against the expenses. The rate of thesalt water can be increased by recycling of salt water.

In a process according to the present invention sea water is pressurizedbefore it flows through the membrane module. Then the sea water togetherwith the fresh water which has been transported through the membrane,will expand through a turbine. The pump as well as the turbine will havean efficiency of less than 1, and energy will consequently be lost inthese unity operations.

To reduce the loss when large quantities of sea water first have to becompressed, and then expanded through a turbine, pressure exchange canbe used. In pressure exchange the pressure in outgoing diluted sea wateris used to compress incoming sea water. Only a quantity of watercorresponding to the fresh water which flows through the membrane willpass through the turbine, and a far smaller turbine can therefore beused. The high pressure pump for pressurizing the sea water iscompletely eliminated.

Finally the invention describes a plant for the production of electricpower, where the plant comprises water filters for purifying a saltcontaining feed stream and a feed stream containing less salt, one ormore semi-permeable membranes or membrane modules, as well as anarrangement for direct hydraulic transmission of an osmotic pressure.

FIG. 1 describes a PRO plant wherein fresh water as well as sea water isfed into separate water filters prior to the streams are passing by oneanother on each side of a semi-permeable membrane. A portion of themixture of permeate and salt water with elevated pressure is passed to aturbine for the production of electric power. The balance of thepermeate stream is passed to a pressure exchanger where incoming seawater is pressurized. The pressurized sea water is then fed into themembrane module.

FIG. 2 shows the stream pattern for cross-stream in a spiral module.

FIG. 3 shows stream lines in a spiral module.

FIG. 4 shows the build-up of the interior structure of a membrane, anon-porous layer, called diffusion skin, and one porous layer.

FIG. 5 shows the relation between pressure on the one side of themembrane which is in contact with a quantity salt containing water (thesea water side), and osmotic flux. FIG. 5 shows the values S which areacceptable for economical power production when A is 10⁻¹¹ m/s/Pa and Bis 3·10⁻⁸ m/s. This or higher values of A are considered as necessary.Consequently S must have a value of 0.001 m or lower. Laboratorymeasurements have shown that the membranes intended for reverse osmosis,which gives the best performance in pressure retarded osmosis, haveS-values around 0.003 m. This means that S has to be improved with afactor of 3 or better in relation to these membranes. Lower values of Bwill to some extent modify the requirement for S.

FIG. 6 shows effect as function of pressure on the sea water side for aprocess with conditions as given in table 2.

FIG. 7 shows concentration relations along membrane for PRO withconditions as given in table 2 (the salt concentrations on the freshwater side are hardly visible).

FIG. 8 shows volume flux of water through the membrane for a processwith conditions given in table 2.

The necessary values for the salt permeability, B, the waterpermeability, A, the structure parameter, S, and the thickness of thediffusion films will also apply to possible fiber membranes. A principaldrawing for fibre membranes will be as for spirals with exception ofthat which concerns the use of flow breaking distance nets.

Examples of energy production:

The mixing zone for salt water and fresh water can be considered asadiabatic, i.e. there is no heat exchange (dq=0) with the surroundings.Since the mixing enthalpy is approximately zero, and work (dw), but notheat, is extracted from the mixture, it is obtained from the energypreservation law:

dE=c _(P) dT=dq+dw=dw   Equation (5)

wherein dE is the change in the inner energy of the total system andc_(P) is the heat capacity of the system.

Extraction of work will according to equation (5) lead to a certain ofcooling. If one mole of fresh water with 52.5 J/mole is reversibly mixedwith three moles of salt water, the diluted salt water will be cooleddown with 0.17° C. In a real process optimised for energy production permixing unit, half of the reversible work will be taken out. This leadsto a cooling of the mixture of less than 0.1° C.

As mentioned above, only 50% of the possible mixing free energy will beutilized in a practical device to maximize the energy production.Further, energy will be lost by operation of the process. With theassumption that 20% of the energy which is produced in the mixing unitis lost in the process (loss because of friction, operation of pumps,turbines, etc.) about 20 J per mole of fresh water which passes throughthe process could be produced. This causes an energy production for somelocations based on mean flow of water transport according to the presentinvention as illustrated in table 1.

TABLE 1 Examples of possible power plants based on average water flowExample of rivers Water flow (m³/s) Power production (MW) Small localriver  10  10 Namsen (Norway) 290 300 Glomma (Norway) 720 750 Rhine(Germany) 2 200   2 400   Mississippi (USA) 18 000   19 000  

Examples of operating variables:

For calculation of water and salt transport through the membrane as wellas energy production per area unit of membrane, it is necessary to havereal values of the different parameters which describe the actualmembrane, the shape of the membrane module, parameters describing theprocess conditions, as well as some physical data. Necessary parametersfor the calculations are summarized in table 2.

All calculations in the following are carried out on the basis of 1 m²membrane area. Because the water and salt fluxes through the membrane inmost cases are considerable in relation to the incoming rates of saltwater and fresh water, the concentrations, and therefore also the fluxesthrough the membrane, will vary along the membrane. To allow for thisthe membrane is divided into 20 cells of equal size for calculationpurposes. The concentrations and rates of salt water and fresh water,respectively, to the first cell, and the sea water pressure on themembrane, are given by the input conditions, see table 2. The fluxes ofwater and salt for these conditions are then calculated iteratively fromcell to cell by means of the necessary equations.

The salt water rate, Q, out from the last cell, defines the rate out ofthe process. The difference between out-rate and in-rate for salt water,and the pressure on the salt water side indicates the produced work. Theexploitation ratio of fresh water is indicated by the difference betweenfresh water rate in and out in relation to fresh water rate in.

TABLE 2 Necessary parameters for model calculations of pressure retardedosmosis. Example Symbol Unit value Parameter A m/Pa/s 10⁻¹¹ Waterpermeability in the membrane B m/s 10⁻⁸  Salt permeability through themembrane x m 0.0005 Thickness of the porous layer φ 0.5 Porosity inporous layer τ 1.5 Tortuosity in porous layer d_(sjø) m 0.00005Thickness of diffusion film on the sea water side d_(f) m 0.00005Thickness of diffusion film on the fresh water side T ° C. 3 Process(water) temperature p_(sjø) Pa 13 · 10⁵  Pressure on the sea water sidec_(sjø) ^(inn) mol/m³ 549 Incoming concentration of salt in salt waterc_(f) ^(inn) mol/m³ 0 Incoming concentration of salt in fresh waterQ_(inn) m³/s  9 · 10⁻⁶ Volume rate of fresh water in on the membrane F 3Feed ratio between salt water and fresh water D_(s) m²/s 7.5 · 10⁻¹⁰Coefficient of diffusion for salt (NaCl) S m ≦0.0015 Structure parameter

For each single set of parameters fluxes and rates are calculated asstated above. For determination of optimal sea water pressure the seawater pressure is always varied with other conditions constant.

In the calculations pressure loss through the membrane module because ofthe flow resistance has not been considered. Neither has the efficiencyof the pump which pressurizes the sea water and the turbine whichproduces energy from the process been considered. Produced work aspresented is therefore related to the energy production during themixing process, and is not equal to the real work that can be extractedfrom a real process. Such dimensions has to be estimated for the plantsin question.

The coefficient of diffusion for salt is increasing with approximately80% when the temperature increases from 3 to 20° C., but do not changemuch with the concentration of salt. The coefficient of diffusion at 0.1moles/l is therefore used in all calculations. As an example ofcalculations a basis point has been taken in the conservative parametervalues stated in table 2. At these conditions the membrane produces 2.74W/m², and 23% of the fresh water which is supplied to the membrane istransported over to the sea water side. FIG. 1 shows the effect per areaunit of membrane as a function of the pressure on the sea water side. Asshown on the figure the effect has a relatively flat optimum areabetween 13 and 18 bars. By selecting a little more favourable values forthe membrane thickness, film thickness and temperature, the energyproduction can easily be higher than 5 W/m².

The concentrations over the membrane from the inlet side and to theoutlet are shown on FIG. 7 for a sea water pressure of 13 bars. Becausethe salt leakage through this membrane is small in this example, theincrease of the salt concentration on the fresh water side is hardlynoticeable, and reaches a discharge concentration of 0.5 moles/m³.Correspondingly the concentration polarization on the fresh water sidecan be fully neglected.

On the other hand, the concentration polarization on the sea water sideis considerable, and gives a concentration drop just below 100 moles/m³.Correspondingly there is a concentration drop of almost 150 moles/m³over the carrier. The driving concentration difference over the skin ofthe membrane corresponds to the concentration difference between thesurface of the skin against the sea water and the side of the adjacentporous layer which faces against the sea water, see FIG. 7, and amountsto approximately 320 moles/m³, or barely 60% of the concentrationdifference between sea water and fresh water. This illustrates theimportance of reducing the polarization effects. This is achieved byminimizing the thickness of the diffusion film on the sea water side(high flow velocity and good stirring), and the thickness of thecarrier.

FIG. 8 shows the volume flux of water through the membrane as a functionof dimensionless position from the inlet side. As the figure shows, thewater flux changes relatively little, and the reason for this is thatthe driving concentration difference also is relatively constant alongthe membrane, see FIG. 7.

1. A semi-permeable membrane for forward osmosis or pressure retardedosmosis, the membrane comprising one thin layer of a non-porous materialas a diffusion skin, and at least one layer of a porous material,wherein the porous layer has, when water wetted, a porosity φ,thickness×(m), and tortuosity τ in relation to one another as given byx·τ=φ·S   Equation (1) where S has a value of 0.0015 meter or lower, theporosity φ has an average value of more than 50%, the tortuosity τ isless than 2.5, a water permeability of the porous layer is greater than1×10⁻¹¹ m/s/Pa, and a salt permeability of the porous layer is less than3×10⁻⁸ m/s.
 2. The semi-permeable membrane according to claim 1, whereinthe membrane has a thickness of less than 150 μm.
 3. The semi-permeablemembrane according to claim 1, wherein the membrane has a thickness ofless than 100 μm.
 4. The semi-permeable membrane according to claim 1,comprising a diffusion film thickness of less than 60 μm.
 5. Thesemi-permeable membrane according to claim 1, comprising a diffusionfilm thickness of less than 30 μm.
 6. The semi-permeable membraneaccording to claim 1, wherein the porous layer of the membrane compriseshollow fibers with an outside diameter from 0.05 to 0.5 mm.
 7. Asemi-permeable membrane for pressure retarded osmosis, the membranecomprising one thin layer of a non-porous material as a diffusion skin,and at least one layer of a porous material, wherein the porous layerhas, when water wetted, a porosity φ, thickness×(m) and tortuosity τ inrelation to one another as given byx·τ=φ·S   Equation (1) where S has a value of 0.0015 meter or lower,wherein the porous layer, when an amount of a first water feed streamcontaining salt is contacted with the diffusion skin, has propertiesrelated to a salt permeability parameter B defined by:B=(φ·D·(dc/dx)/τ−J·c)·1/Δc _(s)   Equation (2) wherein: A is the waterpermeability and is greater than 1×10⁻¹¹ m/s/Pa, B is the saltpermeability (m/s) and is less than 3×10⁻⁸ m/s, Δc_(s) is the saltconcentration difference over the diffusion skin (moles/cm³), φ is theporosity and has an average value of more than 50%, x is the thicknessof the porous layer (m), J is the water flux (m/s), C is the saltconcentration (moles/cm³), D is the diffusion coefficient of the salt(m²/s), τ is the tortuosity and is less than 2.5, where the efficiencyof the membrane in pressure retarded osmosis for a given value of awater permeability, A (m/s/Pa), can be expressed by an integration ofEquation (2) to yield:Δc _(s) /c _(b)=exp(−d _(s) ·J/D)/{1+B·[(exp(d _(f) ·J/D+S·J/D)−exp(−d_(s) ·J/D)]/J} wherein: c_(b) is the difference in salt concentrationbetween a second water feed stream and said first water feed stream,wherein said second water feed stream contains less salt than said firstwater feed stream (moles/cm³), d_(f) and d_(s) are the thickness (μm) ofthe diffusion films on a side of the membrane contacting the secondwater feed stream and a side of the membrane contacting the first waterfeed stream, respectively, and Δc_(s)/c_(b) is the efficiency of themembrane in pressure retarded osmosis for a given value of the waterpermeability.
 8. The semi-permeable membrane according to claim 7,wherein the membrane has a thickness which is less than 150 μm.
 9. Thesemi-permeable membrane according to claim 7, wherein the membrane has athickness of less than 100 μm.
 10. The semi-permeable membrane accordingto claim 7, comprising a diffusion film thickness of less than 60 μm.11. The semi-permeable membrane according to claim 7, comprising adiffusion film thickness of less than 30 μm.
 12. The semi-permeablemembrane according to claim 7, wherein the porous layer of the membranecomprises hollow fibers with an outside diameter from 0.05 to 0.5 mm.13. A semi-permeable membrane for pressure retarded osmosis, themembrane comprising one thin layer of a non-porous material as adiffusion skin, and at least one layer of a porous material, wherein theporous layer has, when water wetted, a porosity φ, thickness×(m) andtortuosity τ in relation to one another as given byx·τ=φ·S   Equation (1) where S has a value of 0.0015 meter or lower, theporosity φ has an average value of more than 50%, the tortuosity τ isless than 2.5, a water permeability of the porous layer is greater than1×10⁻¹¹ m/s/Pa, and a salt permeability of the porous layer is less than3×10⁻⁸ m/s, and wherein the membrane is configured for creating electricpower through use of osmotic hydraulic elevated pressure created by saidpressure retarded osmosis for driving at least one power turbine. 14.The semi-permeable membrane according to claim 13, wherein the membranehas a thickness which is less than 150 μm.
 15. The semi-permeablemembrane according to claim 13, wherein the membrane has a thickness ofless than 100 μm.
 16. The semi-permeable membrane according to claim 13,comprising a diffusion film thickness of less than 60 μm.
 17. Thesemi-permeable membrane according to claim 13, comprising a diffusionfilm thickness of less than 30 μm.
 18. The semi-permeable membraneaccording to claim 13, wherein the porous layer of the membranecomprises hollow fibers with an outside diameter from 0.05 to 0.5 mm.